A food firm is researching the profitability of introducing six new "healthy choice" food products (call them x, y, z, a, b, c). The firm currently has idle resource capacity on labor, machinery, and land of 100 hours, 300 hours, and 30,000 square feet, respec- tively. Hence, producing any or all of the new products will help solve the costs of excess capacity. The selling prices, total costs, resource requirements, and endow- ments for the production technology are summarized on the next page.
New Product
|
Resource (Unit)
|
x
|
y
|
z
|
a
|
b
|
c
|
|
Labor (hours)
|
0.50
|
0.10
|
1.00
|
0.45
|
0.2
|
0.15
|
|
Machinery (hours)
|
1.00
|
0.45
|
3.50
|
1.00
|
1.10
|
2.00
|
|
Land (sq ft)
|
100
|
200
|
50
|
25
|
10
|
75
|
|
Unit Costs ($)
|
10
|
3
|
33
|
22
|
12
|
9
|
|
Unit Price ($)
|
12
|
4
|
36
|
23
|
15
|
11
|
Food products y and z are complements in the sense that for every unit of y produced and sold, 2 units of z must be produced and sold. Also, the firm requires that the amount of product c produced and sold be at least 50% of the total units of products a and b that are produced and sold. Set up a LP model that will result in a solution that maximizes total profit from the sale of any combination of these food products, subject to all constraints that were specified (use Solver).